|
Search: id:A038458
|
|
|
| A038458 |
|
Consider the equation q^x-p^x=1 where p,q are successive primes; solve for x; the smallest such x is 0.567148... which occurs when p=113, q=127. Sequence gives decimal expansion of this value of x. |
|
+0
4
|
|
| 5, 6, 7, 1, 4, 8, 1, 3, 0, 2, 0, 2, 0, 1, 7, 7, 1, 4, 6, 4, 6, 8, 4, 6, 8, 7, 5, 5, 3, 3, 4, 8, 2, 5, 6, 4, 5, 8, 6, 7, 9, 0, 2, 4, 9, 3, 8, 8, 6, 3, 8, 2, 0, 6, 8, 4, 0, 2, 8, 5, 2, 2, 1, 8, 2, 6, 8, 0, 6, 7, 6, 6, 3, 3, 8, 2, 7, 6, 9, 2, 1, 5, 0, 8, 8, 6, 9, 7, 3, 8, 5, 3, 6, 4, 2, 6, 4, 4
(list; cons; graph; listen)
|
|
|
OFFSET
|
0,1
|
|
|
COMMENT
|
Sometimes called the Smarandache constant.
Is this constant rational or irrational? I conjecture it is irrational. - Sukanto Bhattacharya (susant5au(AT)yahoo.com.au), Apr 28 2008
|
|
REFERENCES
|
M. L. Perez, Five Smarandache Conjectures On Primes, Arizona State University, Special Collections.
F. Smarandache, Conjectures which Generalize Andrica's Conjecture, Octogon, Vol. 7, No. 1, 173-176, 1999.
F. Smarandache, Collected Papers, Vol. III, Abaddaba, pages 105-108, 2000.
|
|
LINKS
|
M. L. Perez et al., eds., Smarandache Notions Journal
F. Smarandache, Collected Papers, Vol. III.
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Eric Weisstein's World of Mathematics, Smarandache Constant
|
|
EXAMPLE
|
Generalizes Andrica's conjecture p(n+1)^(1/2)-p(n)^(1/2)<1 to p(n+1)^a-p(n)^a<1 if a < this number.
|
|
CROSSREFS
|
Sequence in context: A081820 A019978 A030178 this_sequence A021642 A095942 A139395
Adjacent sequences: A038455 A038456 A038457 this_sequence A038459 A038460 A038461
|
|
KEYWORD
|
nonn,cons
|
|
AUTHOR
|
M. I. Petrescu (mipetrescu(AT)yahoo.com)
|
|
|
Search completed in 0.002 seconds
|
